If $ 1, w, w^{2} $ are three cube roots of unity, then $ \left(1-\omega+\omega^{2}\right)\left(1+\omega-\omega^{2}\right) $ is

Question

If $ 1, w, w^{2} $ are three cube roots of unity, then $ \left(1-\omega+\omega^{2}\right)\left(1+\omega-\omega^{2}\right) $ is, $ 11 $, $ 02 $, $ 03 $, $ 04 $

MARKS App · Accepted Answer

We have, ( 1 − ω + ω 2 ) ( 1 + ω − ω 2 ) → ( 1 ) We know that, 1 + ω + ω 2 = 0 ⇒ 1 − ω + ω 2 = − 2 ω { subtracting 2 ω both the sides } ⇒ 1 + ω − ω 2 = − 2 ω 2 { subtracting 2 ω 2 both the sides } So, Eq. (1) becomes = ( − 2 ω ) ( − 2 ω 2 ) = 4 ω 3 = 4 { Since, ω 3 = 1 }

Search any question & find its solution

Looking for more such questions to practice?